# ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by **Romain Gaillac** and **François-Xavier Coudert** at CNRS / Chimie
ParisTech.

If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (*J. Phys. Condens. Matter*, 2016, 28, 275201) and give the
website URL.

ELATE is open source software. Any queries or comments are welcome at

## Summary of the properties

### Input: stiffness matrix (coefficients in GPa) of TiPN3 (Materials Project id mp-989613)

388 113 66 0 0 0 113 196 97 0 0 0 66 97 448 0 0 0 0 0 0 53 0 0 0 0 0 0 91 0 0 0 0 0 0 34

### Average properties

Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|

Voigt | K_{V} = 176 GPa | E_{V} = 221.86 GPa | G_{V} = 86 GPa | ν_{V} = 0.2899 |

Reuss | K_{R} = 159.67 GPa | E_{R} = 166.41 GPa | G_{R} = 62.737 GPa | ν_{R} = 0.3263 |

Hill | K_{H} = 167.84 GPa | E_{H} = 194.39 GPa | G_{H} = 74.368 GPa | ν_{H} = 0.30696 |

### Eigenvalues of the stiffness matrix

λ_{1} |
λ_{2} |
λ_{3} |
λ_{4} |
λ_{5} |
λ_{6} |
---|---|---|---|---|---|

34 GPa | 53 GPa | 91 GPa | 130.93 GPa | 351.48 GPa | 549.59 GPa |

### Variations of the elastic moduli

Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | ||||||
---|---|---|---|---|---|---|---|---|---|

E_{min} | E_{max} |
β_{min} | β_{max} | G_{min} | G_{max} |
ν_{min} | ν_{max} | ||

Value | 109.53 GPa | 399.68 GPa | 1.2307 TPa^{–1} | 3.7589 TPa^{–1} | 34 GPa | 173.67 GPa | 0.031211 | 0.67946 | Value |

Anisotropy | 3.649 | 3.0543 | 5.108 | 21.7700 | Anisotropy | ||||

Axis | -0.6231 0.7821 -0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
1.0000 -0.0002 0.0000 |
0.7071 -0.0000 -0.7071 |
0.0000 0.0000 1.0000 |
-0.8584 0.5130 -0.0000 |
Axis |

0.0002 1.0000 0.0001 |
-0.7071 0.0002 -0.7071 |
-1.0000 0.0000 0.0000 |
-0.5130 -0.8584 -0.0000 |
Second axis |

## Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

## Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

## Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

## Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane